A 'steam bath' is an enclosure which is kept around 45°C. It is fed with some sort of steam generator which produces thick clouds of mist.

Historically,
steam baths, not to be confused with saunas, have been a popular way of
bathing for thousands of years. They were known to the
ancient Greeks and have long traditions in both Turkey and Russia.

In our modern world, steam baths or saunas can be found in most spas and gyms. They are also becoming increasingly popular for
home installation. Thanks to recent developments in steam
generator technology steam baths can be installed in almost any residential bathroom.

However, as in the paragraph above, we often hear the terms "steam
bath", "steam shower" and "sauna" used pretty interchangeably. But, do
they actually mean the same thing?

Not necessarily.

Strictly speaking, a "steam bath" is an enclosure which is kept around
45°C. It is fed with some sort of steam generator
which produces thick clouds of mist.
Obviously, the room has to be fairly well sealed to prevent the steam
from escaping and also to prevent moisture damage to the surrounding
structure at the same time.

A steam shower is basically the same as a steam bath but on a smaller
scale. It is usually big enough for one or two people and can
be installed in a standard shower stall. Steam showers are
often used for residential steam baths.

The Sauna...The Bath

A steam bath is sometimes called a steam sauna but, a sauna is actually
a different type of bath. A Finnish sauna produces a dry heat
and is also much hotter than a steam bath. Saunas are usually
heated between 70°C and 100°C. Steam is
produced within a sauna by pouring water over hot rocks, but usually
the air is quite dry -- approximately 20% humidity as compared to
nearly 100% humidity in a steam bath.

Many people would like to have a steam shower
installed in their house but are understandably concerned about the
build-up of humidity. However, if you have a fairly modern
bathroom with an enclosed shower stall, you can easily install a steam
shower without any concerns about excess humidity.

The steam shower will have to be an enclosed unit to contain the
moisture and to allow it to drain off. If you don't have an
enclosed shower stall or bathtub, existing bathtubs can still be
modified to accommodate a steam shower. On the other hand, if
you have a large bathroom, a better alternative might be to just
install a separate steam shower.

Steam Generator

Fortunately, the steam generator does not have to be in the
bathroom. It can be installed up to 40 feet away from the
steam shower. The generator needs an adequate electrical
connection, and some models also need to be connected to a drain.

Finally, the steam generator is connected to a steam head which is
installed in the steam bath itself. Some modern steam heads
have built in controls while others are controlled with an external
unit. As you can understand, it is more convenient to have
the control inside the steam bath itself so that you can make
adjustments as needed.

Since steam baths are, indeed, so relaxing you will likely spend more
time there than in a normal shower. This means you should
also think about installing some kind of seating arrangement.
The steam heads should be installed away from the seating area so that
the possibility of being scalded with the hot steam is reduced.

All of this installation work will require specialized plumbing and
electrical skills. Before making the decision to install a
steam shower in your house, consult both a plumber and an electrician
to see if it is feasible.

They will also be able to give you a pretty accurate estimate of the
cost involved.